In this article, we improved the nonlinear weight of the classical third-order WENO scheme by using the limiter of the MUSCL scheme and got a new WENO scheme, the WENO-F scheme, and developed three new nonlinear multiple-parameter weight functions by improving the nonlinear weight of WENO-JS, WENO-Z, and WENO-Z+ schemes. After selecting appropriate parameters of these new weight functions, three new high-resolution schemes are comparing with three kinds of classical WENO schemes. Theoretical analysis and numerical results show that the new scheme with these multiparameter functional weights can achieve third-order convergence in smooth regions. And the new scheme has lower dissipation and better resolution than the classical third-order WENO schemes for smooth and discontinuous solutions.

中文翻译：

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改进三阶 WENO 方案的新功能权重

在本文中，我们利用 MUSCL 方案的限制器改进了经典三阶 WENO 方案的非线性权重，得到了一个新的 WENO 方案，即 WENO-F 方案，并通过改进开发了三个新的非线性多参数权重函数WENO-JS、WENO-Z 和 WENO-Z+ 方案的非线性权重。在为这些新的权重函数选择合适的参数后，三种新的高分辨率方案与三种经典的 WENO 方案进行了比较。理论分析和数值结果表明，具有这些多参数函数权重的新方案可以在平滑区域内实现三阶收敛。对于平滑和不连续解，新方案比经典的三阶 WENO 方案具有更低的耗散和更好的分辨率。